The present invention is directed to the selective removal of hydrogen sulfide from a gas stream. In particular, the present invention is directed to the selective removal of hydrogen sulfide from a high pressure gas stream which also contains carbon dioxide by using a metal chelate solution. Through operation at high pressures, the present invention may be used in situations where low pressure operation would be costly and time-consuming, such as in the removal of hydrogen sulfide from the gas stream of a natural gas production well.